Instantons and Four-Manifolds

Häftad, Engelska, 2011

Del i serien Mathematical Sciences Research Institute Publications

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Beskrivning

From the reviews of the first edition: "This book exposes the beautiful confluence of deep techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional manifolds, compact spaces locally modeled on the world in which we live and operate...

Produktinformation

Utgivningsdatum:2011-12-14
Mått:155 x 235 x 16 mm
Vikt:346 g
Format:Häftad
Språk:Engelska
Serie:Mathematical Sciences Research Institute Publications
Antal sidor:194
Upplaga:2
Förlag:Springer-Verlag New York Inc.
ISBN:9781461397052

Utforska kategorier

Topologi inom Naturvetenskap och teknik

Innehållsförteckning

to the First Edition.- §1 Fake ?4.- Differentiable structures.- Topological 4-manifolds.- Differentiable 4-manifolds.- A surgical failure.- §2 The Yang-Mills Equations.- Connections.- Topological quantum numbers.- The Yang-Mills functional.- Line bundles.- Donaldson’s Theorem.- §3 Manifolds of Connections.- Sobolev spaces.- Reducible connections.- A slice theorem.- The parametrized moduli space.- The moduli space.- §4 Cones on ??2.- Slices again.- Structure of the singular point.- Perturbing the metric.- §5 Orientability.- Index bundles.- Components of.- The element — 1.- §6 Introduction to Taubes’ Theorem.- Instantons on S4.- A grafting procedure.- Tools from analysis.- Analytic properties of SDYME.- §7 Taubes’ Theorem.- Blowing up the metric.- The eigenvalue estimate.- The linearized equation.- Taubes’ projection.- §8 Compactness.- Compactness and regularity.- Measuring concentrated curvature.- Compactness in M.- §9 The Collar Theorem.- Decay estimates.- Conformal deformations.- Exponential gauges.- Connectivity of the collar.- § 10 The Technique of Fintushel and Stern.- The moduli space for SO(3) bundles.- Reducible connections.- Analytic details.- Appendix A The Group of Sobolev Gauge Transformations.- Appendix B The Pontrjagin-Thom Construction.- Appendix C Weitzenböck Formulas.- Appendix D The Removability of Singularities.- Appendix E Topological Remarks.